Research

23/11/2024

Research Topics
Functional Analysis, Operator Spaces
Harmonic Analysis, Probability Methods in Analysis
Random Matrices, Determinantaux Point Processes
Ergodic Theory, Inductively Compact Groups

 

 Preprints

  1. (with Z.F.Lin and M.J.Tan) Fourier dimension of Gaussian multiplicative chaos, arXiv.
  2. (with X.X.Chen, Y.Han and Z.P.Wang) Harmonic analysis of Mandelbrot cascades — in the context of vector-valued martingales, arXiv.
  3. (with Z.F.Lin and K.Wang) Number rigid determinantal point processes induced by generalized Cantor sets, arXiv.
  4. (with Y. Han and Z.P.Wang)  Self-absorption of Hankel systems on monoids –a seemingly universal property, arXiv.
  5. (with G.C.Zhen)  Spectral measure of large random Helson matrices,  arXiv.
  6. (with Z.F.Lin and K.Wang) A Law of large numbers for vector-valued linear statistics of Bergman DPP, arXiv.
  7. (with Y. Han and Z.P.Wang)  Moments of Mandelbrot cascades at critical exponents, arXiv.
  8. (with Y. Han and Z.P.Wang) Holomorphic stability for Carleman pairs of function spaces, arXiv.
  9. (with Y. Han and Z.P.Wang) Complete weighted Bergman spaces have bounded point evaluations, arXiv.
  10. (with Y. Han and Z.P.Wang)  On a class of random sets of positive integers, arXiv.
  11. Radial Toeplitz operators and invariant determinantal point processes on Cayley trees, arXiv.
  12. (with A.I. Bufetov) Patterson-Sullivan measures for point processes and the reconstruction of harmonic functions, arXiv
  13. Ergodic measures and infinite matrices of finite rank, arXiv.
  14. Completely bounded Paley projections on anisotropic Sobolev spaces on tori, arXiv.

 

Publications

  1. (with X.X.Chen, Y.Han and Z.P.Wang) The Mandelbrot-Kahane problem of Benoit Mandelbrot model of turbulence, accepted for publication in Comptes Rendus Mathématiques.
  2. (with Y. Han and Z.P.Wang) Boundedness of Gaussian random sums on trees, accepted for publication in Moscow Math. J.
  3. (with Z.F.Lin and K.Wang) Truncations of Random Unitary Matrices Drawn from Hua-Pickrell Distribution,  Complex Anal. Oper. Theory 17 (2023), no. 1, Paper No. 6, 24 pp.
  4. (with Z.P.Wang) Branching-Toeplitz operators on rooted homogeneous trees,  Tohoku Math.J.  (2) 76 (2024), no.2, 153-174.
  5. (with Y. Han and Z.P.Wang) On Hedenmalm-Shimorin type inequalities, Arkiv för Matematik. 60 (2022), no.2, 351-364. 
  6. (with Z.F.Lin and K.Wang) Gaussian limit for determinantal point processes with J-Hermitian kernels, Sci. China Math. 66 (2023), no.1, Paper No. 6, 24pp.
  7. (with S.L. Fan and L.M. Liao) Stationary determinantal processes: ψ-mixing property and Lq-dimensions,   Stoch. Process. Appl. 151(2022), 1–22.
  8. (with A.I.Bufetov) The Patterson-Sullivan interpolation of pluriharmonic functions for determinantal point processes on complex hyperbolic spaces, Geom.Funct.Anal. 32 (2022), no.2,  135–192.
  9. (with Z.P.Wang)  Hyper-positive definite functions I: scalar case, branching-type stationary stochastic processes, J. Funct. Anal.  282(2022), no.1, Paper No. 109266, 45 pp.
  10. (with Z.P.Wang) The metric projections onto closed convex cones in a Hilbert space,  J. Inst. Math. Jussieu. 21 (2022), no.5, 1617-1650. 
  11. (with K.Wang)  Rigidity of determinantal point processes on the unit disc with sub-Bergman kernels, Israel J. Math. 245 (2021), no.1, 389–408.
  12. (with G. Baverez and A.I. Bufetov) A survey on determinantal point processes. Stochastic analysis, random fields and integrable probability—Fukuoka 2019, 59–88, Adv.Stud.Pure Math., 87,  Math. Soc. Japan, Tokyo, 2021.
  13. (with A.I. Bufetov and F.D. Cunden) Conditional measures for Pfaffian point processes: conditioning on a bounded domain,  Ann. Inst. Henri Poincare Probab. Stat. 57 (2021), no.2, 856–871.
  14. (with C. Bordenave and Y. W. Zhang) Spectral gap of sparse bistochastic matrices with exchangeable rows with application to shuffle-and-fold maps,   Ann. Inst. Henri Poincare Probab. Stat. 56 (2020),no.4, 2971–2995. 
  15. (with A.I. Bufetov and A. Shamov) Kernels of conditional determinantal measures and the proof of the Lyons-Peres conjecture,  J. Eur. Math. Soc. 23(2021),no.5, 1477–1519.
  16. Ergodic measures on spaces of infinite skew-matrices over non-Archimedean local fields,  Groups Geom. Dyn.13 (2019), no.4,1401-1416.    
  17. On a result of Bożejko on extension of positive definite kernels,  Bull.  Lond. Math. Soc. 51 (2019),no.5,798-800.  
  18. (with A.I.Bufetov and P. Nikitin) On number rigidity for Pfaffian point processes, Moscow Math. J. 19(2019), no.2, 217-274.
  19. (with A.H. Fan and S.L. Fan)  Some properties of stationary determinantal point processes on Z,  J. London Math. Soc. (2) 98(2018), no.3, 517–535.
  20. A rigidity property of superpositions involving  determinantal processes, Stoch. Process. Appl. 129(2019), no. 4, 1371–1378.
  21. (with A.I. Bufetov and S.L. Fan) Equivalence of Palm measures for determinantal point processes governed by Bergman kernels,  Probab. Th. Rel. Fields 172(2018), no.1-2, 31–69.
  22. (with A.I. Bufetov) J-Hermitian determinantal point processes: balanced rigidity and balanced Palm equivalence, Math. Annalen 371(2018), no.1-2, 127-188.
  23. (with A.I. Bufetov) Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields,  Compositio Mathematica 153(2017), no.12, 2482-2533.
  24. Rigid stationary determinantal processes in non-Archimedean fields,  Bernoulli 25(1), 2019, 75–88.
  25. (with A.I. Bufetov) Conditional measures of generalized Ginibre point processes, J. Funct. Anal.  272 (2017), no.11, 4671–4708.
  26. (with A.I. Bufetov, Y. Dabrowski) Linear rigidity of stationary stochastic processes,  Ergodic Theory Dynam. Systems 38(2018), no.7,  2493–2507.
  27. (with A.I. Bufetov) Determinantal point processes associated with Hilbert spaces of holomorphic functions,   Commun. Math. Phys., 351(2017), no.1, 1-44.
  28. Infinite Random Matrices and Ergodic decomposition of Finite or Infinite Hua-Pickrell measures,  Advances in Mathematics, 308(2017), pp. 1209-1268. 
  29. Ergodic measures on compact metric spaces for isometric actions by inductively compact groups,  Proc. Amer. Math. Soc. 145 (2017), 1593-1598.
  30. Truncation of Haar random matrices in GL(N, ℤm), Electron. Commun. Probab., 21(2016), Paper No. 49, 6 pp.
  31. (with A.I. Bufetov) The explicit formulae for scaling limits in the ergodic decomposition of infinite Pickrell measures, Arkiv för Matematik, 54 (2016), no.2, 403–435.
  32.  (with A.I. Bufetov) Equivalence of Palm measures for determinantal point processes associated with Hilbert spaces of holomorphic functions, Comptes Rendus Mathématiques, 353 (2015), pp. 551-555.
  33.  On the effect of rearrangement on complex interpolation for families of Banach spaces, Rev. Mat. Iberoamericana, 31 (2015), no. 2 pp. 439–460.
  34.  Duality of uniform approximation property in operator spaces, Illinois J. Math. 58 (2014), no. 4, 1093–1105.
  35.  A non-commutative version of Lépingle -Yor martingale inequality,  Stat & Probab Letters, 91 (2014), 52–54.
  36.  On the OUMD property for the column Hilbert space C, Indiana Univ. Math. J. 61 (2012), 2143-2156.
  37.  On the UMD constants for a class of iterated Lp(Lq) spaces, J. Funct. Anal. 263(8) : 2409-2429, 2012.

 

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